I'm struggling to route the rosette, as I thought would be better idea to route the soundhole and rosette prior to starting bracing the top.

I can't imagine wanting to brace first, then cutting sound hole and rosette: it is much easier to cut the rosette, then sound hole, then brace.

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What do you guys use to carve small circles?

I've got a makita rt0700 router and a dremel routing base, but both tools look too big for this small diameter routing job.

You could use a circle (fly) cutter in a drill press or you could make/modify a router base/circle jig to make allow smaller holes. Typically, the router base interferes with the circle jig for small circles. Depending on the jig/router base, alter the base to accommodate smaller circles.